(a0 (i) A radioactive sample produces 7806 decays per minute at one point in an
ID: 1271030 • Letter: #
Question
(a0 (i) A radioactive sample produces 7806 decays per minute at one point in an experiment and 64.269 days later produces 345 decays per minute. What is the half life of the sample? (ii) What is the decay constant? (iii) What is the mean lifetime of the sample? (b) What fraction of a radioactive sample is left after 4.7362 h. (the half life of the sample is 1.8295 h.) (c) that period of time is required for a radioactive sample to lose 66.667% of its activity? (The half life of this sample is 14.659h.)
Explanation / Answer
a) i)
A = A0 2^(-t/halflife)
345=7806*2^(-64.269/t)
t= 14.28 days
ii) decay constant = ln(2)/t = ln(2)/(14.28*24*60*60)= 5.62E-7
iii) meanlife time = 1/decay = 1/5.62E-7= 1.78E6 s = 20.59 days
b)
% left = 2^(-t/half) = 2^(-4.7362/1.8295)= 0.166
c)
0.66667 = 2^(-t/14.659)
t=8.57 hours
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